Is there a phone switchboard I could use with my neighbour so we only pay one line rental?
I’d caution against doing such a thing. It may be against the terms of service with the phone company to share one line with multiple domiciles like that. If they find out they could cut off service, or even ask you to back pay for the service you should have been paying for. The same may apply to the internet connection. If you want to avoid line rental, get a mobile phone, or a VOIP system. FWIW, I wouldn’t rely on a computer based VOIP for my primary phone. Thinking, you could see if you can get what is called distinctive ring, whereby there are separate dial-in numbers, and each has a different ring pattern. Of course, this second number would not be listed under your name, but your neighbor.